Results 1 to 10 of about 1,398 (233)

On the Infinitely Many Solutions of a Semilinear Elliptic Equation

SIAM Journal on Mathematical Analysis, 1986
Die Autoren untersuchen sphärisch symmetrische Lösungen von \[ (*)\quad \Delta u+f(u)=0\quad im\quad {\mathbb{R}}^ n, \] wobei die Nichtlinearität f die folgenden Bedingungen erfüllt: (1) \(f\in C^ 1\); (2) \(f(u)=k(u)| u|^{\sigma}u+g(u)\) mit \(k(u)=k_+\), \(u\geq 0\); \(k(u)=k_-\), \(u0\), \(k_->0\) \(g(u)=O(| u|^{\gamma})\), \(g'(u)=O(| u|^{\gamma ...
Jones, C., Küpper, T.
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Asymptotic Theory of Singular Semilinear Elliptic Equations

Canadian Mathematical Bulletin, 1984
AbstractNecessary and sufficient conditions are found for the existence of two positive solutions of the semilinear elliptic equation Δu + q(|x|)u = f(x, u) in an exterior domain Ω⊂ℝn, n ≥ 1, where q, f are real-valued and locally Hölder continuous, and f(x, u) is nonincreasing in u for each fixed x∈Ω. An example is the singular stationary Klein-Gordon
Kusano, Takasi, Swanson, Charles A.
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Nontrivial solutions of elliptic semilinear equations¶at resonance

manuscripta mathematica, 2000
The authors consider the following Dirichlet problem \(-\Delta u = \lambda_m +f(x,u)\) in a bounded domain \(\Omega\) with smooth boundary, where \(\lambda _m\) is an eigenvalue of the Laplacian operator in \(\Omega\) with Dirichlet boundary data. They treat the doubly resonant case, both at infinity and zero, \(\lim_{t\to 0}f(x,t)/t= \lim_{t\to \infty}
Perera, Kanishka, Schechter, Martin
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Global Positive Solutions of Semilinear Elliptic Equations

Canadian Journal of Mathematics, 1983
The semilinear elliptic boundary value problem1.1will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where1.2Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded ...
Noussair, Ezzat S., Swanson, Charles A.
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Approximation of Sparse Controls in Semilinear Elliptic Equations

2012
Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for three different discretizations for the control problem are given.
Eduardo Casas, Roland Herzog, Gerd Wachsmuth   +2 more
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On the iterative and minimizing sequences for semilinear elliptic equations (I)

Japan Journal of Industrial and Applied Mathematics, 1995
Les auteurs continuent leur précédente recherche [ibid. 12, No. 2, 309-326 (1995; Zbl 0842.35004)] sur la solution numérique de l'équation elliptique semilinéaire (1) \(-\Delta u= f(u)\) dans \(\Omega\), avec la condition (2) \(u=0\) sur \(\partial \Omega\), où \(\Omega\) est un domaine polygonal à deux dimension.
Mizutani, Akira, Suzuki, Takashi
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ON THE EXISTENCE OF PERIODIC SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS

Russian Academy of Sciences. Sbornik Mathematics, 1994
Summary: Using a variational method, the existence of a solution of the equation \(-\Delta u=g(u)\) in \(\mathbb{R}^{N+1}\) is proved, periodic with respect to one variable and localized with respect to the remaining variables.
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On the Existence of Positive Solutions of Semilinear Elliptic Equations

SIAM Review, 1982
In this paper we study the existence of positive solutions of semilinear elliptic equations. Various possible behaviors of nonlinearity are considered, and in each case nearly optimal multiplicity results are obtained. The results are also interpreted in terms of bifurcation diagrams.
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On Semilinear Elliptic Equations with Hardy-Leray Potentials

Tokyo Journal of Mathematics
Summary: This paper is concerned with a semilinear elliptic equation with the Hardy-Leray potential. We employ the method of moving planes to prove the radial symmetry of positive solutions. Based on this result, we obtain the Liouville theorem in subcritical case. In addition, we find special radial solutions in critical case. All the properties above
Li, Yayun, Lei, Yutian
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Fully linear elliptic equations and semilinear fractionnal elliptic equations

Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient, ...
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